MinT - Best Known (12, 12+8, s)-Nets in Base 4

Best Known (12, 12+8, s)-Nets in Base 4

(12, 12+8, 66)-Net over F₄ — Constructive and digital

Digital (12, 20, 66)-net over F₄, using

trace code for nets [i] based on digital (2, 10, 33)-net over F₁₆, using
- net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]

(12, 12+8, 77)-Net over F₄ — Digital

Digital (12, 20, 77)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4²⁰, 77, F₄, 8) (dual of [77, 57, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(4²⁰, 90, F₄, 8) (dual of [90, 70, 9]-code), using
  - a code from Grasslâ€™s database [i]

(12, 12+8, 752)-Net in Base 4 — Upper bound on s

There is no (12, 20, 753)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 101458 005156 > 4²⁰ [i]