MinT - Best Known (251−151, 251, s)-Nets in Base 4

Best Known (251−151, 251, s)-Nets in Base 4

(251−151, 251, 104)-Net over F₄ — Constructive and digital

Digital (100, 251, 104)-net over F₄, using

t-expansion [i] based on digital (73, 251, 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]

(251−151, 251, 144)-Net over F₄ — Digital

Digital (100, 251, 144)-net over F₄, using

t-expansion [i] based on digital (91, 251, 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]

(251−151, 251, 912)-Net in Base 4 — Upper bound on s

There is no (100, 251, 913)-net in base 4, because

1 times m-reduction [i] would yield (100, 250, 913)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 281634 650354 258276 117809 128344 859017 768659 646606 070041 607095 983965 997494 498915 300043 978264 296544 824572 774458 950992 933928 939036 619449 142782 722860 535968 > 4²⁵⁰ [i]