MinT - Best Known (177−58, 177, s)-Nets in Base 4

Best Known (177−58, 177, s)-Nets in Base 4

(177−58, 177, 240)-Net over F₄ — Constructive and digital

Digital (119, 177, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 59, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(177−58, 177, 528)-Net over F₄ — Digital

Digital (119, 177, 528)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−58, 177, 18368)-Net in Base 4 — Upper bound on s

There is no (119, 177, 18369)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36699 982303 343591 346474 003776 124044 397620 835215 200214 957940 145070 811352 115047 997596 193685 571227 646544 783104 > 4¹⁷⁷ [i]