MinT - Best Known (82, 126, s)-Nets in Base 9

Best Known (82, 126, s)-Nets in Base 9

(82, 126, 740)-Net over F₉ — Constructive and digital

Digital (82, 126, 740)-net over F₉, using

6 times m-reduction [i] based on digital (82, 132, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 66, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(82, 126, 1341)-Net over F₉ — Digital

Digital (82, 126, 1341)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 126, 330333)-Net in Base 9 — Upper bound on s

There is no (82, 126, 330334)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 716202 085284 948884 833257 077383 544468 790045 285115 869615 559381 470211 658586 038395 919978 397394 554444 727411 543767 823330 221665 > 9¹²⁶ [i]