MinT - Best Known (249−149, 249, s)-Nets in Base 4

Best Known (249−149, 249, s)-Nets in Base 4

(249−149, 249, 104)-Net over F₄ — Constructive and digital

Digital (100, 249, 104)-net over F₄, using

t-expansion [i] based on digital (73, 249, 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]

(249−149, 249, 144)-Net over F₄ — Digital

Digital (100, 249, 144)-net over F₄, using

t-expansion [i] based on digital (91, 249, 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]

(249−149, 249, 925)-Net in Base 4 — Upper bound on s

There is no (100, 249, 926)-net in base 4, because

1 times m-reduction [i] would yield (100, 248, 926)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 212140 812996 047993 020241 451704 626506 450240 651685 767265 931537 741928 625715 893136 741170 203631 256567 414181 428728 144116 749623 372053 593741 873805 033068 026468 > 4²⁴⁸ [i]