MinT - Best Known (166−131, 166, s)-Nets in Base 8

Best Known (166−131, 166, s)-Nets in Base 8

(166−131, 166, 65)-Net over F₈ — Constructive and digital

Digital (35, 166, 65)-net over F₈, using

t-expansion [i] based on digital (14, 166, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(166−131, 166, 112)-Net over F₈ — Digital

Digital (35, 166, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(166−131, 166, 661)-Net in Base 8 — Upper bound on s

There is no (35, 166, 662)-net in base 8, because

1 times m-reduction [i] would yield (35, 165, 662)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 112162 075723 935618 425462 977973 864998 106155 739290 046006 230296 387545 552625 868482 021775 317966 381498 263612 936133 420694 034572 029052 061835 047909 493640 974786 > 8¹⁶⁵ [i]