MinT - Best Known (74, 74+31, s)-Nets in Base 3

Best Known (74, 74+31, s)-Nets in Base 3

(74, 74+31, 192)-Net over F₃ — Constructive and digital

Digital (74, 105, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 35, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(74, 74+31, 277)-Net over F₃ — Digital

Digital (74, 105, 277)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+31, 6513)-Net in Base 3 — Upper bound on s

There is no (74, 105, 6514)-net in base 3, because

1 times m-reduction [i] would yield (74, 104, 6514)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41 796315 948307 573029 831362 770597 296878 823592 227801 > 3¹⁰⁴ [i]