MinT - Best Known (118, 196, s)-Nets in Base 4

Best Known (118, 196, s)-Nets in Base 4

(118, 196, 130)-Net over F₄ — Constructive and digital

Digital (118, 196, 130)-net over F₄, using

t-expansion [i] based on digital (105, 196, 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]

(118, 196, 292)-Net over F₄ — Digital

Digital (118, 196, 292)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 196, 5413)-Net in Base 4 — Upper bound on s

There is no (118, 196, 5414)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10114 587121 680859 429267 719865 798183 033989 390353 622220 741744 704056 716268 333315 437112 787432 678055 266750 349665 087254 010544 > 4¹⁹⁶ [i]