MinT - Best Known (254−162, 254, s)-Nets in Base 4

Best Known (254−162, 254, s)-Nets in Base 4

(254−162, 254, 104)-Net over F₄ — Constructive and digital

Digital (92, 254, 104)-net over F₄, using

t-expansion [i] based on digital (73, 254, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(254−162, 254, 144)-Net over F₄ — Digital

Digital (92, 254, 144)-net over F₄, using

t-expansion [i] based on digital (91, 254, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(254−162, 254, 732)-Net in Base 4 — Upper bound on s

There is no (92, 254, 733)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 877 817619 405322 385722 533635 539442 515898 737088 436241 877502 675483 903091 505189 547239 150776 339741 917007 741760 606450 092507 267906 195515 391397 337928 749710 348680 > 4²⁵⁴ [i]