MinT - Best Known (62−29, 62, s)-Nets in Base 7

Best Known (62−29, 62, s)-Nets in Base 7

(62−29, 62, 104)-Net over F₇ — Constructive and digital

Digital (33, 62, 104)-net over F₇, using

trace code for nets [i] based on digital (2, 31, 52)-net over F₄₉, using
- net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(62−29, 62, 156)-Net over F₇ — Digital

Digital (33, 62, 156)-net over F₇, using

trace code for nets [i] based on digital (2, 31, 78)-net over F₄₉, using
- net from sequence [i] based on digital (2, 77)-sequence over F₄₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 2 and N(F) ≥ 78, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(62−29, 62, 4838)-Net in Base 7 — Upper bound on s

There is no (33, 62, 4839)-net in base 7, because

1 times m-reduction [i] would yield (33, 61, 4839)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 3559 344350 069067 918357 815682 712503 960383 491381 135741 > 7⁶¹ [i]