MinT - Best Known (122−86, 122, s)-Nets in Base 4

Best Known (122−86, 122, s)-Nets in Base 4

(122−86, 122, 56)-Net over F₄ — Constructive and digital

Digital (36, 122, 56)-net over F₄, using

t-expansion [i] based on digital (33, 122, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(122−86, 122, 65)-Net over F₄ — Digital

Digital (36, 122, 65)-net over F₄, using

t-expansion [i] based on digital (33, 122, 65)-net over F₄, using
- net from sequence [i] based on digital (33, 64)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 65, using
    - Drinfeld modules of rank 1 [i]

(122−86, 122, 253)-Net in Base 4 — Upper bound on s

There is no (36, 122, 254)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 29 787449 470870 267812 516516 039741 482036 457138 615747 214211 426136 387506 873902 > 4¹²² [i]