MinT - Best Known (91, 91+81, s)-Nets in Base 8

Best Known (91, 91+81, s)-Nets in Base 8

(91, 91+81, 256)-Net over F₈ — Constructive and digital

Digital (91, 172, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 86, 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]

(91, 91+81, 352)-Net over F₈ — Digital

Digital (91, 172, 352)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+81, 16320)-Net in Base 8 — Upper bound on s

There is no (91, 172, 16321)-net in base 8, because

1 times m-reduction [i] would yield (91, 171, 16321)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 26850 442324 686436 543068 607369 919232 480925 448918 919498 907850 527268 023920 334022 026184 796607 575589 619077 871710 527401 977469 437253 583481 790417 217693 069843 658392 > 8¹⁷¹ [i]