MinT - Best Known (138−39, 138, s)-Nets in Base 3

Best Known (138−39, 138, s)-Nets in Base 3

(138−39, 138, 246)-Net over F₃ — Constructive and digital

Digital (99, 138, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 46, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(138−39, 138, 399)-Net over F₃ — Digital

Digital (99, 138, 399)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−39, 138, 10908)-Net in Base 3 — Upper bound on s

There is no (99, 138, 10909)-net in base 3, because

1 times m-reduction [i] would yield (99, 137, 10909)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 232466 777105 791921 274695 886417 456625 677271 846951 041621 400271 544523 > 3¹³⁷ [i]