MinT - Best Known (34, 34+114, s)-Nets in Base 9

Best Known (34, 34+114, s)-Nets in Base 9

(34, 34+114, 81)-Net over F₉ — Constructive and digital

Digital (34, 148, 81)-net over F₉, using

t-expansion [i] based on digital (32, 148, 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]

(34, 34+114, 128)-Net over F₉ — Digital

Digital (34, 148, 128)-net over F₉, using

t-expansion [i] based on digital (33, 148, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(34, 34+114, 794)-Net in Base 9 — Upper bound on s

There is no (34, 148, 795)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1765 409816 113938 288314 066192 782673 439077 466586 801224 804304 596759 295352 555803 104090 876615 362499 823874 201834 206815 628159 347134 259524 372998 807065 > 9¹⁴⁸ [i]