MinT - Best Known (53, 53+120, s)-Nets in Base 8

Best Known (53, 53+120, s)-Nets in Base 8

(53, 53+120, 98)-Net over F₈ — Constructive and digital

Digital (53, 173, 98)-net over F₈, using

t-expansion [i] based on digital (37, 173, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(53, 53+120, 144)-Net over F₈ — Digital

Digital (53, 173, 144)-net over F₈, using

t-expansion [i] based on digital (45, 173, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(53, 53+120, 1293)-Net in Base 8 — Upper bound on s

There is no (53, 173, 1294)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 782326 791198 657254 684562 819530 215589 187102 290270 149739 988898 987610 321019 099435 263891 640592 067598 942932 413320 490529 761160 882793 518591 915927 148794 370388 752432 > 8¹⁷³ [i]