MinT - Best Known (147−48, 147, s)-Nets in Base 4

Best Known (147−48, 147, s)-Nets in Base 4

(147−48, 147, 240)-Net over F₄ — Constructive and digital

Digital (99, 147, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 49, 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]

(147−48, 147, 458)-Net over F₄ — Digital

Digital (99, 147, 458)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−48, 147, 15897)-Net in Base 4 — Upper bound on s

There is no (99, 147, 15898)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31856 277067 248357 240047 534586 615774 145874 007422 482761 046303 101194 871053 956045 211227 571161 > 4¹⁴⁷ [i]