MinT - Best Known (66, 66+77, s)-Nets in Base 9

Best Known (66, 66+77, s)-Nets in Base 9

(66, 66+77, 165)-Net over F₉ — Constructive and digital

Digital (66, 143, 165)-net over F₉, using

t-expansion [i] based on digital (64, 143, 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]

(66, 66+77, 195)-Net over F₉ — Digital

Digital (66, 143, 195)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+77, 6888)-Net in Base 9 — Upper bound on s

There is no (66, 143, 6889)-net in base 9, because

1 times m-reduction [i] would yield (66, 142, 6889)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3194 352270 908619 984611 131072 973685 420602 614987 202586 972307 109178 576990 348442 498367 039758 602201 255968 243066 186525 211407 546855 126397 066609 > 9¹⁴² [i]