MinT - Best Known (10, 10+7, s)-Nets in Base 8

Best Known (10, 10+7, s)-Nets in Base 8

Digital (10, 17, 160)-net over F₈, using

1 times m-reduction [i] based on digital (10, 18, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 9, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

Digital (10, 17, 178)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8¹⁷, 178, F₈, 7) (dual of [178, 161, 8]-code), using
- 15 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 14 times 0) [i] based on linear OA(8¹⁶, 162, F₈, 7) (dual of [162, 146, 8]-code), using
  - trace code [i] based on linear OA(64⁸, 81, F₆₄, 7) (dual of [81, 73, 8]-code), using
    - extended algebraic-geometric code AG_e(F,73P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 81, using
      - sharp bound on the number of rational points on curves with genus 1 [i]

There is no (10, 17, 17011)-net in base 8, because

1 times m-reduction [i] would yield (10, 16, 17011)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 281 476284 897032 > 8¹⁶ [i]