MinT - Best Known (248−144, 248, s)-Nets in Base 4

Best Known (248−144, 248, s)-Nets in Base 4

(248−144, 248, 104)-Net over F₄ — Constructive and digital

Digital (104, 248, 104)-net over F₄, using

t-expansion [i] based on digital (73, 248, 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]

(248−144, 248, 144)-Net over F₄ — Digital

Digital (104, 248, 144)-net over F₄, using

t-expansion [i] based on digital (91, 248, 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]

(248−144, 248, 1033)-Net in Base 4 — Upper bound on s

There is no (104, 248, 1034)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 211973 260848 932377 539944 684966 731518 954712 584520 491007 954873 352483 762707 571456 396638 663730 752677 546944 287072 630249 324349 059217 571651 095993 538315 382000 > 4²⁴⁸ [i]