MinT - Best Known (256−138, 256, s)-Nets in Base 4

Best Known (256−138, 256, s)-Nets in Base 4

(256−138, 256, 130)-Net over F₄ — Constructive and digital

Digital (118, 256, 130)-net over F₄, using

t-expansion [i] based on 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]

(256−138, 256, 168)-Net over F₄ — Digital

Digital (118, 256, 168)-net over F₄, using

t-expansion [i] based on digital (115, 256, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(256−138, 256, 1458)-Net in Base 4 — Upper bound on s

There is no (118, 256, 1459)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13817 615365 981175 475407 114799 886537 278358 829551 672447 667246 622301 865140 094488 506214 139079 436738 865362 772529 271733 940355 785694 969851 472586 776079 596816 303600 > 4²⁵⁶ [i]