MinT - Best Known (225−107, 225, s)-Nets in Base 4

Best Known (225−107, 225, s)-Nets in Base 4

(225−107, 225, 130)-Net over F₄ — Constructive and digital

Digital (118, 225, 130)-net over F₄, using

t-expansion [i] based on digital (105, 225, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(225−107, 225, 187)-Net over F₄ — Digital

Digital (118, 225, 187)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−107, 225, 2362)-Net in Base 4 — Upper bound on s

There is no (118, 225, 2363)-net in base 4, because

1 times m-reduction [i] would yield (118, 224, 2363)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 739 053746 921449 758661 614221 182208 966378 997103 136618 783773 425457 613917 683407 499571 084863 545573 365541 575392 371523 984551 814387 303835 733860 > 4²²⁴ [i]