MinT - Best Known (12, 12+76, s)-Nets in Base 32

Best Known (12, 12+76, s)-Nets in Base 32

(12, 12+76, 120)-Net over F₃₂ — Constructive and digital

Digital (12, 88, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 88, 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]

(12, 12+76, 129)-Net over F₃₂ — Digital

Digital (12, 88, 129)-net over F₃₂, using

net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(12, 12+76, 1463)-Net in Base 32 — Upper bound on s

There is no (12, 88, 1464)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 910970 832116 370591 175639 570166 391654 943935 108025 538279 953027 170079 951305 057700 712557 560783 182471 537224 503807 610504 913410 997122 869665 > 32⁸⁸ [i]