MinT - Best Known (122, 122+49, s)-Nets in Base 3

Best Known (122, 122+49, s)-Nets in Base 3

(122, 122+49, 252)-Net over F₃ — Constructive and digital

Digital (122, 171, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 57, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(122, 122+49, 451)-Net over F₃ — Digital

Digital (122, 171, 451)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(122, 122+49, 11723)-Net in Base 3 — Upper bound on s

There is no (122, 171, 11724)-net in base 3, because

1 times m-reduction [i] would yield (122, 170, 11724)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1290 291065 948934 369423 149661 950173 053843 012003 112313 416037 789235 933152 440727 008833 > 3¹⁷⁰ [i]