MinT - Best Known (131−65, 131, s)-Nets in Base 9

Best Known (131−65, 131, s)-Nets in Base 9

(131−65, 131, 165)-Net over F₉ — Constructive and digital

Digital (66, 131, 165)-net over F₉, using

t-expansion [i] based on digital (64, 131, 165)-net over F₉, using
- net from sequence [i] based on digital (64, 164)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 64 and N(F) ≥ 165, using
    - T₄ from the second tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(131−65, 131, 255)-Net over F₉ — Digital

Digital (66, 131, 255)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−65, 131, 12014)-Net in Base 9 — Upper bound on s

There is no (66, 131, 12015)-net in base 9, because

1 times m-reduction [i] would yield (66, 130, 12015)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11282 223547 593443 253766 559197 671790 791462 367129 987429 463974 425678 899187 701888 217033 232842 498433 926360 997515 358767 922867 261185 > 9¹³⁰ [i]