MinT - Best Known (254−140, 254, s)-Nets in Base 4

Best Known (254−140, 254, s)-Nets in Base 4

(254−140, 254, 130)-Net over F₄ — Constructive and digital

Digital (114, 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]

(254−140, 254, 165)-Net over F₄ — Digital

Digital (114, 254, 165)-net over F₄, using

t-expansion [i] based on digital (109, 254, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(254−140, 254, 1314)-Net in Base 4 — Upper bound on s

There is no (114, 254, 1315)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 857 357552 321530 349619 702283 338760 785529 049541 357539 902856 286675 009777 326544 497225 689728 309658 759519 647860 353942 612223 824656 228883 464136 264442 819023 119328 > 4²⁵⁴ [i]