MinT - Best Known (79−66, 79, s)-Nets in Base 7

Best Known (79−66, 79, s)-Nets in Base 7

(79−66, 79, 21)-Net over F₇ — Constructive and digital

Digital (13, 79, 21)-net over F₇, using

net from sequence [i] based on digital (13, 20)-sequence over F₇, using
- Niederreiter sequence [i]

(79−66, 79, 48)-Net over F₇ — Digital

Digital (13, 79, 48)-net over F₇, using

net from sequence [i] based on digital (13, 47)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 13 and N(F) ≥ 48, using
  - an algebraic function field by Teo [i]

(79−66, 79, 118)-Net in Base 7 — Upper bound on s

There is no (13, 79, 119)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁷⁹, 119, S₇, 66), but
- the linear programming bound shows that MÂ â‰¥ 145721 934604 598341 564421 495611 527507 878739 330308 830223 125505 981686 116204 181150 099208 602068 496614 343638 899899 600379 / 23783 642505 784746 446056 401241 584175 625957 376000 > 7⁷⁹ [i]