MinT - Best Known (111−36, 111, s)-Nets in Base 4

Best Known (111−36, 111, s)-Nets in Base 4

(111−36, 111, 240)-Net over F₄ — Constructive and digital

Digital (75, 111, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 37, 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]

(111−36, 111, 377)-Net over F₄ — Digital

Digital (75, 111, 377)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−36, 111, 12978)-Net in Base 4 — Upper bound on s

There is no (75, 111, 12979)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 743859 423813 886744 392522 258068 869359 757199 660237 083380 933633 834223 > 4¹¹¹ [i]