MinT - Best Known (49, 96, s)-Nets in Base 16

Best Known (49, 96, s)-Nets in Base 16

(49, 96, 516)-Net over F₁₆ — Constructive and digital

Digital (49, 96, 516)-net over F₁₆, using

trace code for nets [i] based on digital (1, 48, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(49, 96, 578)-Net over F₁₆ — Digital

Digital (49, 96, 578)-net over F₁₆, using

trace code for nets [i] based on digital (1, 48, 289)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 288)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
    - sharp bound on the number of rational points on curves with genus 1 [i]

(49, 96, 59130)-Net in Base 16 — Upper bound on s

There is no (49, 96, 59131)-net in base 16, because

1 times m-reduction [i] would yield (49, 95, 59131)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 463040 447593 563488 734001 083966 485180 739939 606729 755960 101366 317605 555806 325749 211026 080316 734655 080520 550086 311496 > 16⁹⁵ [i]