MinT - Best Known (247−155, 247, s)-Nets in Base 4

Best Known (247−155, 247, s)-Nets in Base 4

(247−155, 247, 104)-Net over F₄ — Constructive and digital

Digital (92, 247, 104)-net over F₄, using

t-expansion [i] based on digital (73, 247, 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]

(247−155, 247, 144)-Net over F₄ — Digital

Digital (92, 247, 144)-net over F₄, using

t-expansion [i] based on digital (91, 247, 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]

(247−155, 247, 762)-Net in Base 4 — Upper bound on s

There is no (92, 247, 763)-net in base 4, because

1 times m-reduction [i] would yield (92, 246, 763)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13737 085364 369131 531830 535814 320868 920826 230939 859077 863772 741023 822656 681773 245257 387294 966641 667439 499822 299622 838599 505850 448342 667622 627374 804872 > 4²⁴⁶ [i]