MinT - Best Known (260−169, 260, s)-Nets in Base 4

Best Known (260−169, 260, s)-Nets in Base 4

(260−169, 260, 104)-Net over F₄ — Constructive and digital

Digital (91, 260, 104)-net over F₄, using

t-expansion [i] based on digital (73, 260, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(260−169, 260, 144)-Net over F₄ — Digital

Digital (91, 260, 144)-net over F₄, using

net from sequence [i] based on digital (91, 143)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
  - Drinfeld modules of rank 1 [i]

(260−169, 260, 700)-Net in Base 4 — Upper bound on s

There is no (91, 260, 701)-net in base 4, because

1 times m-reduction [i] would yield (91, 259, 701)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 867253 092099 689743 705074 079522 009774 866001 007791 401022 360605 648005 631657 168241 948459 377275 564449 236186 193735 317708 244234 977627 250960 538708 978540 407840 108558 > 4²⁵⁹ [i]