MinT - Best Known (11, 66, s)-Nets in Base 7

Best Known (11, 66, s)-Nets in Base 7

(11, 66, 19)-Net over F₇ — Constructive and digital

Digital (11, 66, 19)-net over F₇, using

net from sequence [i] based on digital (11, 18)-sequence over F₇, using
- Niederreiter sequence [i]

(11, 66, 38)-Net over F₇ — Digital

Digital (11, 66, 38)-net over F₇, using

t-expansion [i] based on digital (9, 66, 38)-net over F₇, using
- net from sequence [i] based on digital (9, 37)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 9 and N(F) ≥ 38, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(11, 66, 121)-Net in Base 7 — Upper bound on s

There is no (11, 66, 122)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁶⁶, 122, S₇, 55), but
- the linear programming bound shows that MÂ â‰¥ 37079 616886 430573 106530 371695 955888 720032 761391 449532 270606 747505 739945 258421 557427 872844 227479 466385 003509 360768 817453 637208 818090 558037 161385 364518 328602 / 618 800815 150652 930422 169446 148769 641355 591201 475540 708208 629083 267738 964025 118675 409624 717118 018615 > 7⁶⁶ [i]