MinT - Best Known (104, 104+146, s)-Nets in Base 4

Best Known (104, 104+146, s)-Nets in Base 4

(104, 104+146, 104)-Net over F₄ — Constructive and digital

Digital (104, 250, 104)-net over F₄, using

t-expansion [i] based on digital (73, 250, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(104, 104+146, 144)-Net over F₄ — Digital

Digital (104, 250, 144)-net over F₄, using

t-expansion [i] based on digital (91, 250, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(104, 104+146, 1017)-Net in Base 4 — Upper bound on s

There is no (104, 250, 1018)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 417027 594985 640412 034650 921639 913226 898921 932855 655472 067689 380819 926956 457004 362967 955188 954937 013345 771733 264117 134030 952077 981722 985533 300333 387525 > 4²⁵⁰ [i]