MinT - Best Known (237−139, 237, s)-Nets in Base 4

Best Known (237−139, 237, s)-Nets in Base 4

(237−139, 237, 104)-Net over F₄ — Constructive and digital

Digital (98, 237, 104)-net over F₄, using

t-expansion [i] based on digital (73, 237, 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]

(237−139, 237, 144)-Net over F₄ — Digital

Digital (98, 237, 144)-net over F₄, using

t-expansion [i] based on digital (91, 237, 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]

(237−139, 237, 957)-Net in Base 4 — Upper bound on s

There is no (98, 237, 958)-net in base 4, because

1 times m-reduction [i] would yield (98, 236, 958)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12563 601555 763002 543114 075494 277732 765461 973884 706243 795877 394240 454767 344525 664015 143903 823253 554052 886622 445661 184013 563419 755439 103853 954910 > 4²³⁶ [i]