MinT - Best Known (153−103, 153, s)-Nets in Base 8

Best Known (153−103, 153, s)-Nets in Base 8

(153−103, 153, 98)-Net over F₈ — Constructive and digital

Digital (50, 153, 98)-net over F₈, using

t-expansion [i] based on digital (37, 153, 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]

(153−103, 153, 144)-Net over F₈ — Digital

Digital (50, 153, 144)-net over F₈, using

t-expansion [i] based on digital (45, 153, 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]

(153−103, 153, 1362)-Net in Base 8 — Upper bound on s

There is no (50, 153, 1363)-net in base 8, because

1 times m-reduction [i] would yield (50, 152, 1363)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 192136 026037 009769 876278 886041 255484 701369 876821 325156 131093 270736 274536 996921 347492 160728 264356 781654 196645 266676 680125 660355 239645 248432 > 8¹⁵² [i]