MinT - Best Known (66, 66+64, s)-Nets in Base 9

Best Known (66, 66+64, s)-Nets in Base 9

(66, 66+64, 200)-Net over F₉ — Constructive and digital

Digital (66, 130, 200)-net over F₉, using

trace code for nets [i] based on digital (1, 65, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(66, 66+64, 262)-Net over F₉ — Digital

Digital (66, 130, 262)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+64, 12014)-Net in Base 9 — Upper bound on s

There is no (66, 130, 12015)-net in base 9, because

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]