MinT - Best Known (79−50, 79, s)-Nets in Base 32

Best Known (79−50, 79, s)-Nets in Base 32

(79−50, 79, 120)-Net over F₃₂ — Constructive and digital

Digital (29, 79, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 79, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(79−50, 79, 216)-Net in Base 32 — Constructive

(29, 79, 216)-net in base 32, using

5 times m-reduction [i] based on (29, 84, 216)-net in base 32, using
- base change [i] based on digital (5, 60, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]

(79−50, 79, 257)-Net over F₃₂ — Digital

Digital (29, 79, 257)-net over F₃₂, using

t-expansion [i] based on digital (28, 79, 257)-net over F₃₂, using
- net from sequence [i] based on digital (28, 256)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 28 and N(F) ≥ 257, using
    - a curve from the manYPoints database [i]

(79−50, 79, 258)-Net in Base 32

(29, 79, 258)-net in base 32, using

5 times m-reduction [i] based on (29, 84, 258)-net in base 32, using
- base change [i] based on digital (15, 70, 258)-net over F₆₄, using
  - net from sequence [i] based on digital (15, 257)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 15 and N(F) ≥ 258, using
      - a curve from the manYPoints database [i]

(79−50, 79, 18717)-Net in Base 32 — Upper bound on s

There is no (29, 79, 18718)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 80780 671630 918138 047963 052500 728224 431113 466739 095431 851219 822294 615888 386651 171405 932130 579208 954415 351029 927813 950665 > 32⁷⁹ [i]