MinT - Best Known (53, 53+47, s)-Nets in Base 16

Best Known (53, 53+47, s)-Nets in Base 16

(53, 53+47, 520)-Net over F₁₆ — Constructive and digital

Digital (53, 100, 520)-net over F₁₆, using

trace code for nets [i] based on digital (3, 50, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(53, 53+47, 642)-Net over F₁₆ — Digital

Digital (53, 100, 642)-net over F₁₆, using

2 times m-reduction [i] based on digital (53, 102, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 51, 321)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(53, 53+47, 95776)-Net in Base 16 — Upper bound on s

There is no (53, 100, 95777)-net in base 16, because

1 times m-reduction [i] would yield (53, 99, 95777)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 161406 049536 757920 684819 257642 572382 235107 357519 551393 884276 173471 479901 710364 793579 858078 055327 471955 564955 194749 669216 > 16⁹⁹ [i]