MinT - Best Known (107−84, 107, s)-Nets in Base 32

Best Known (107−84, 107, s)-Nets in Base 32

(107−84, 107, 120)-Net over F₃₂ — Constructive and digital

Digital (23, 107, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 107, 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]

(107−84, 107, 128)-Net in Base 32 — Constructive

(23, 107, 128)-net in base 32, using

1 times m-reduction [i] based on (23, 108, 128)-net in base 32, using
- base change [i] based on digital (5, 90, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(107−84, 107, 185)-Net over F₃₂ — Digital

Digital (23, 107, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 107, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(107−84, 107, 3617)-Net in Base 32 — Upper bound on s

There is no (23, 107, 3618)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 113475 773273 331660 610531 419364 967228 108053 875748 487718 637364 592061 122612 036355 125353 157494 844407 214565 619579 199017 928245 296205 747540 475015 401274 673739 926272 777984 > 32¹⁰⁷ [i]