MinT - Best Known (250−156, 250, s)-Nets in Base 4

Best Known (250−156, 250, s)-Nets in Base 4

(250−156, 250, 104)-Net over F₄ — Constructive and digital

Digital (94, 250, 104)-net over F₄, using

t-expansion [i] based on digital (73, 250, 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]

(250−156, 250, 144)-Net over F₄ — Digital

Digital (94, 250, 144)-net over F₄, using

t-expansion [i] based on digital (91, 250, 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]

(250−156, 250, 783)-Net in Base 4 — Upper bound on s

There is no (94, 250, 784)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 343921 831529 899038 827581 340367 270531 873395 939422 336847 834550 391529 650621 319897 057893 588845 572570 060604 247811 953646 580151 287652 962547 490473 530645 799756 > 4²⁵⁰ [i]