MinT - Best Known (256−151, 256, s)-Nets in Base 4

Best Known (256−151, 256, s)-Nets in Base 4

(256−151, 256, 130)-Net over F₄ — Constructive and digital

Digital (105, 256, 130)-net over F₄, using

net from sequence [i] based on digital (105, 129)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
  - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(256−151, 256, 144)-Net over F₄ — Digital

Digital (105, 256, 144)-net over F₄, using

t-expansion [i] based on digital (91, 256, 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]

(256−151, 256, 1007)-Net in Base 4 — Upper bound on s

There is no (105, 256, 1008)-net in base 4, because

1 times m-reduction [i] would yield (105, 255, 1008)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3570 232144 813605 833855 881384 599560 454589 610660 000684 418025 119519 716103 239110 748397 767899 147047 566044 298332 428588 670869 842356 252463 835296 722855 646127 473179 > 4²⁵⁵ [i]