MinT - Best Known (257−95, 257, s)-Nets in Base 4

Best Known (257−95, 257, s)-Nets in Base 4

(257−95, 257, 200)-Net over F₄ — Constructive and digital

Digital (162, 257, 200)-net over F₄, using

t-expansion [i] based on digital (161, 257, 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]

(257−95, 257, 476)-Net over F₄ — Digital

Digital (162, 257, 476)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−95, 257, 11610)-Net in Base 4 — Upper bound on s

There is no (162, 257, 11611)-net in base 4, because

1 times m-reduction [i] would yield (162, 256, 11611)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13448 688419 108876 468897 410553 597366 678263 755860 786667 936133 144745 647993 360147 220192 115952 717323 705703 615489 826590 823343 712555 116818 681495 550687 446344 937536 > 4²⁵⁶ [i]