MinT - Best Known (103−72, 103, s)-Nets in Base 32

Best Known (103−72, 103, s)-Nets in Base 32

(103−72, 103, 120)-Net over F₃₂ — Constructive and digital

Digital (31, 103, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 103, 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]

(103−72, 103, 177)-Net in Base 32 — Constructive

(31, 103, 177)-net in base 32, using

t-expansion [i] based on (25, 103, 177)-net in base 32, using
- 5 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
  - base change [i] based on digital (7, 90, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(103−72, 103, 273)-Net over F₃₂ — Digital

Digital (31, 103, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 103, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(103−72, 103, 9309)-Net in Base 32 — Upper bound on s

There is no (31, 103, 9310)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 107638 605561 428960 288891 756522 395234 078282 827369 691122 813891 481753 169223 072977 726394 030306 779738 022453 014563 726904 937634 935951 549178 930739 777479 714560 260902 > 32¹⁰³ [i]