MinT - Best Known (156−43, 156, s)-Nets in Base 3

Best Known (156−43, 156, s)-Nets in Base 3

(156−43, 156, 264)-Net over F₃ — Constructive and digital

Digital (113, 156, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 52, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(156−43, 156, 480)-Net over F₃ — Digital

Digital (113, 156, 480)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−43, 156, 14403)-Net in Base 3 — Upper bound on s

There is no (113, 156, 14404)-net in base 3, because

1 times m-reduction [i] would yield (113, 155, 14404)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 90 031487 316275 184082 209752 325620 606515 701045 276439 229253 220352 805495 903849 > 3¹⁵⁵ [i]