MinT - Best Known (16, 16+11, s)-Nets in Base 8

Best Known (16, 16+11, s)-Nets in Base 8

Digital (16, 27, 160)-net over F₈, using

3 times m-reduction [i] based on digital (16, 30, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 15, 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 (16, 27, 202)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8²⁷, 202, F₈, 11) (dual of [202, 175, 12]-code), using
- 7 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 6 times 0) [i] based on linear OA(8²⁶, 194, F₈, 11) (dual of [194, 168, 12]-code), using
  - trace code [i] based on linear OA(64¹³, 97, F₆₄, 11) (dual of [97, 84, 12]-code), using
    - extended algebraic-geometric code AG_e(F,85P) [i] based on function field F/F₆₄ with g(F) = 2 and N(F) ≥ 97, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(16, 27, 258)-net in base 8, using

There is no (16, 27, 18482)-net in base 8, because

1 times m-reduction [i] would yield (16, 26, 18482)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 302254 411406 974273 185660 > 8²⁶ [i]