MinT - Best Known (42, 42+34, s)-Nets in Base 4

Best Known (42, 42+34, s)-Nets in Base 4

(42, 42+34, 90)-Net over F₄ — Constructive and digital

Digital (42, 76, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 38, 45)-net over F₁₆, using
- net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]

(42, 42+34, 92)-Net over F₄ — Digital

Digital (42, 76, 92)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+34, 1162)-Net in Base 4 — Upper bound on s

There is no (42, 76, 1163)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5763 912773 141804 671257 010716 912040 273550 242000 > 4⁷⁶ [i]