MinT - Best Known (253−151, 253, s)-Nets in Base 4

Best Known (253−151, 253, s)-Nets in Base 4

(253−151, 253, 104)-Net over F₄ — Constructive and digital

Digital (102, 253, 104)-net over F₄, using

t-expansion [i] based on digital (73, 253, 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]

(253−151, 253, 144)-Net over F₄ — Digital

Digital (102, 253, 144)-net over F₄, using

t-expansion [i] based on digital (91, 253, 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]

(253−151, 253, 949)-Net in Base 4 — Upper bound on s

There is no (102, 253, 950)-net in base 4, because

1 times m-reduction [i] would yield (102, 252, 950)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 54 042439 266202 038129 129260 691087 438159 170196 369173 917034 028178 822569 883695 563571 382536 621242 391915 455650 790829 532265 389347 028470 425273 349642 655863 434440 > 4²⁵² [i]