MinT - Best Known (98−62, 98, s)-Nets in Base 9

Best Known (98−62, 98, s)-Nets in Base 9

(98−62, 98, 81)-Net over F₉ — Constructive and digital

Digital (36, 98, 81)-net over F₉, using

t-expansion [i] based on digital (32, 98, 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]

(98−62, 98, 128)-Net over F₉ — Digital

Digital (36, 98, 128)-net over F₉, using

t-expansion [i] based on digital (33, 98, 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]

(98−62, 98, 1593)-Net in Base 9 — Upper bound on s

There is no (36, 98, 1594)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3279 796395 033006 143830 441873 189448 297281 255359 054201 658686 761112 126138 938317 818386 815586 752497 > 9⁹⁸ [i]