MinT - Best Known (118−82, 118, s)-Nets in Base 4

Best Known (118−82, 118, s)-Nets in Base 4

(118−82, 118, 56)-Net over F₄ — Constructive and digital

Digital (36, 118, 56)-net over F₄, using

t-expansion [i] based on digital (33, 118, 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]

(118−82, 118, 65)-Net over F₄ — Digital

Digital (36, 118, 65)-net over F₄, using

t-expansion [i] based on digital (33, 118, 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]

(118−82, 118, 258)-Net in Base 4 — Upper bound on s

There is no (36, 118, 259)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 118304 035578 964784 286406 394997 125026 924519 053045 219019 679829 389276 871616 > 4¹¹⁸ [i]