MinT - Best Known (49, 136, s)-Nets in Base 9

Best Known (49, 136, s)-Nets in Base 9

(49, 136, 81)-Net over F₉ — Constructive and digital

Digital (49, 136, 81)-net over F₉, using

t-expansion [i] based on digital (32, 136, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(49, 136, 168)-Net over F₉ — Digital

Digital (49, 136, 168)-net over F₉, using

net from sequence [i] based on digital (49, 167)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 49 and N(F) ≥ 168, using
  - Drinfeld modules of rank 1 [i]

(49, 136, 2064)-Net in Base 9 — Upper bound on s

There is no (49, 136, 2065)-net in base 9, because

1 times m-reduction [i] would yield (49, 135, 2065)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 675 193697 352904 406681 816032 552425 343601 866609 437392 554940 654360 624744 396377 673701 936518 080239 362054 400175 879238 522021 889475 976345 > 9¹³⁵ [i]