MinT - Best Known (33, 62, s)-Nets in Base 16

Best Known (33, 62, s)-Nets in Base 16

(33, 62, 518)-Net over F₁₆ — Constructive and digital

Digital (33, 62, 518)-net over F₁₆, using

trace code for nets [i] based on digital (2, 31, 259)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(33, 62, 642)-Net over F₁₆ — Digital

Digital (33, 62, 642)-net over F₁₆, using

trace code for nets [i] based on digital (2, 31, 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]

(33, 62, 71095)-Net in Base 16 — Upper bound on s

There is no (33, 62, 71096)-net in base 16, because

1 times m-reduction [i] would yield (33, 61, 71096)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 28 270745 571319 067757 662407 091842 738479 771945 041561 795432 942981 207462 648386 > 16⁶¹ [i]