MinT - Best Known (256−95, 256, s)-Nets in Base 4

Best Known (256−95, 256, s)-Nets in Base 4

(256−95, 256, 200)-Net over F₄ — Constructive and digital

Digital (161, 256, 200)-net over F₄, using

net from sequence [i] based on digital (161, 199)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 161 and N(F) ≥ 200, using
  - F₇ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(256−95, 256, 468)-Net over F₄ — Digital

Digital (161, 256, 468)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−95, 256, 11271)-Net in Base 4 — Upper bound on s

There is no (161, 256, 11272)-net in base 4, because

1 times m-reduction [i] would yield (161, 255, 11272)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3356 493601 596944 834987 879647 464157 635685 160810 052881 174335 934603 617039 694007 355232 998648 257015 991177 597714 902223 042784 063475 802639 392535 841146 051116 365440 > 4²⁵⁵ [i]