MinT - Best Known (37, 37+107, s)-Nets in Base 8

Best Known (37, 37+107, s)-Nets in Base 8

(37, 37+107, 98)-Net over F₈ — Constructive and digital

Digital (37, 144, 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]

(37, 37+107, 121)-Net over F₈ — Digital

Digital (37, 144, 121)-net over F₈, using

net from sequence [i] based on digital (37, 120)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 121, using
  - a curve from the manYPoints database [i]

(37, 37+107, 770)-Net in Base 8 — Upper bound on s

There is no (37, 144, 771)-net in base 8, because

1 times m-reduction [i] would yield (37, 143, 771)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1387 510671 669680 712111 962848 147714 252793 058653 217009 963268 853715 742673 946202 049153 690536 306571 395003 165875 010276 913532 434470 739328 > 8¹⁴³ [i]