MinT - Best Known (36, 61, s)-Nets in Base 8

Best Known (36, 61, s)-Nets in Base 8

Digital (36, 61, 256)-net over F₈, using

1 times m-reduction [i] based on digital (36, 62, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 31, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(36, 61, 258)-net in base 8, using

Digital (36, 61, 289)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8⁶¹, 289, F₈, 25) (dual of [289, 228, 26]-code), using
- 88 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 0, 0, 0, 1, 8 times 0, 1, 14 times 0, 1, 17 times 0, 1, 19 times 0, 1, 21 times 0) [i] based on linear OA(8⁵⁴, 194, F₈, 25) (dual of [194, 140, 26]-code), using
  - trace code [i] based on linear OA(64²⁷, 97, F₆₄, 25) (dual of [97, 70, 26]-code), using
    - extended algebraic-geometric code AG_e(F,71P) [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]

There is no (36, 61, 24751)-net in base 8, because

1 times m-reduction [i] would yield (36, 60, 24751)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 532749 502296 551907 261842 757846 707111 542478 322818 431111 > 8⁶⁰ [i]