MinT - Best Known (254−136, 254, s)-Nets in Base 4

Best Known (254−136, 254, s)-Nets in Base 4

(254−136, 254, 130)-Net over F₄ — Constructive and digital

Digital (118, 254, 130)-net over F₄, using

t-expansion [i] based on digital (105, 254, 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]

(254−136, 254, 168)-Net over F₄ — Digital

Digital (118, 254, 168)-net over F₄, using

t-expansion [i] based on digital (115, 254, 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]

(254−136, 254, 1490)-Net in Base 4 — Upper bound on s

There is no (118, 254, 1491)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 838 915647 310362 117869 791003 998380 680257 582500 812993 391747 380734 625316 820218 014402 587822 143264 516680 269197 349952 062154 756694 671488 252805 041682 141197 559948 > 4²⁵⁴ [i]