MinT - Best Known (213−100, 213, s)-Nets in Base 2

Best Known (213−100, 213, s)-Nets in Base 2

(213−100, 213, 57)-Net over F₂ — Constructive and digital

Digital (113, 213, 57)-net over F₂, using

t-expansion [i] based on digital (110, 213, 57)-net over F₂, using
- net from sequence [i] based on digital (110, 56)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 69, N(F)Â =Â 48, 1 place with degree 2, and 8 places with degree 6 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]

(213−100, 213, 72)-Net over F₂ — Digital

Digital (113, 213, 72)-net over F₂, using

t-expansion [i] based on digital (110, 213, 72)-net over F₂, using
- net from sequence [i] based on digital (110, 71)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 110 and N(F) ≥ 72, using
    - Drinfeld modules of rank 1 [i]

(213−100, 213, 243)-Net in Base 2 — Upper bound on s

There is no (113, 213, 244)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2²¹³, 244, S₂, 100), but
- the linear programming bound shows that MÂ â‰¥ 1497 079260 199888 243041 749449 030518 858517 186262 320438 889975 998087 858063 671296 / 92413 151121 > 2²¹³ [i]