MinT - Best Known (226−151, 226, s)-Nets in Base 4

Best Known (226−151, 226, s)-Nets in Base 4

(226−151, 226, 104)-Net over F₄ — Constructive and digital

Digital (75, 226, 104)-net over F₄, using

t-expansion [i] based on digital (73, 226, 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]

(226−151, 226, 112)-Net over F₄ — Digital

Digital (75, 226, 112)-net over F₄, using

t-expansion [i] based on digital (73, 226, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(226−151, 226, 553)-Net in Base 4 — Upper bound on s

There is no (75, 226, 554)-net in base 4, because

1 times m-reduction [i] would yield (75, 225, 554)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3074 462057 761146 816430 371009 771938 721425 241816 667612 935617 877949 929903 054234 693391 253432 800380 756966 079584 018244 561410 353397 955906 120960 > 4²²⁵ [i]